You are both kind of right. There is no statute that explicitly allows for a grace period and you are right to tell your tenant that you expect your rent by the date it is due. There is, however, a regulation, 940 C.M.R. 3.17(6)(a), that prohibits landlords from collecting a late fee unless rent is 30 days late. Be careful not to violate this law as doing so is a violation of the consumer protection law, G.L. ch. 93A. If the late payments are a chronic problem that is unacceptable to you, you could argue that they constitute a violation of the lease (assuming there is one and it provides for a date by which payment is due every month). This could be a basis for an eviction, although that could take several months and be potentially costly. The tenant would also have an opportunity to raise certain defenses to the eviction. Therefore, you may want to weigh the inconvenience of getting paid late (but at least you're getting paid) versus the potential expense and uncertainty of an eviction action.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.